JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f(x) = 2^{10}\cdot x + 1\) and \(g(x) = 3^{10}\cdot x - 1\) . If \((fog)(x)=x\), then \(x\) is equal to
- A \(\frac{{{3^{10}} - 1}}{{{3^{10}} - {2^{ - 10}}}}\)
- B \(\frac{{{2^{10}} - 1}}{{{2^{10}} - {3^{ - 10}}}}\)
- C \(\frac{{1 - {3^{ - 10}}}}{{{2^{10}} - {3^{ - 10}}}}\)
- D \(\frac{{1 - {2^{ - 10}}}}{{{3^{10}} - {2^{ - 10}}}}\)
Answer & Solution
Correct Answer
(D) \(\frac{{1 - {2^{ - 10}}}}{{{3^{10}} - {2^{ - 10}}}}\)
Step-by-step Solution
Detailed explanation
\(f\left( {g\left( x \right)} \right) = x\) \( \Rightarrow f\left( {{3^{10}}x - 1} \right) = {2^{10}}\left( {{3^{10}}.x - 1} \right) + 1 = x\) \( \Rightarrow {2^{10}}\left( {{3^{10}}x - 1} \right) + 1 = x\) \( \Rightarrow x\left( {{6^{10}} - 1} \right) = {2^{10}} - 1\)…
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